Let be a continuous onto function satisfying for all

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f:\mathbb{R}\to\mathbb{R}

be a continuous onto function satisfying

f(x)+f(-x)=0

for all

x\in\mathbb{R}

. If

f(-3)=2

and

f(5)=4

, then in

[-5,5]

the equation

f(x)=0

has (a) exactly three real roots (b) exactly two real roots (c) at least five real roots (d) at least three real roots